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429 views

DSP, discrete time, how to calculate the frequency

this is from Digital Signal Processing, 4th ed, Sanjit K Mitra, problem 2.39b. The question is: Determine the fundamental period of $x[n] = cos(0.6n\pi + 0.3\pi)$ Since x[n], is in square brackets, ...
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1answer
17 views

Top and bottom power spectral density of a height profile

Imagine I have a simple 1D height profile which is NOT symmetric. Now, what is truly important for me is to know what are the frequency content of the top profile (i.e. a cut profile above the ...
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0answers
40 views

Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary time series(in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary parts of ...
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1answer
18 views

The bandwidth of the signal $x(t)$.

The bandwidth (B) of the signal $x(t)$ is the range of frequencies (measured on the positive semi-axis) in which $X(\omega)$ takes values ​​different from $0$. Very often $X(\omega)$ is different from ...
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0answers
30 views

Parseval's theorem.

We consider two signal $h(t)$ and $g(t)$ such that $$\int_{-\infty}^\infty |g(t)|^2dt<+\infty$$ $$\int_{-\infty}^\infty |f(t)|^2dt<+\infty$$ Parseval's theorem states that: ...
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1answer
352 views

How do I find transfer function of a discrete-time system when its state-space form is given?

I read this and this Wikipedia pages, but both of them are explaining continuous-time systems. My question is about discrete-time case. For example, given the state-space equations of the second ...
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4answers
195 views

Compressive sensing with non square matrices

I'm implementing the algorithm in the following paper: "Compressive sensing for wideband cognitive radios" http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04218361 However I've run into a ...
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31 views

Using l1 magic toolbox for compressive sensing : Positive definite matricies.

I'm trying to use l1 magic to reconstruct an image from a single pixel camera I've developed. The test functions used are random binary patterns projected onto the object scene, so each pattern is ...
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1answer
21 views

Is there a way to modify the exponential smoothing function to account for varying sample rates?

I am using a simple exponential smoothing formula to smooth a signal. X(n) = a * S(n) + ( 1 - a ) * X(n-1) However on certain setups, the sample rate is much ...
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1answer
3k views

The definition of NMSE (normalized mean square error)

Many papers use the NMSE function without ever explicitly defining it. I have always assumed that $$MSE(x,y)=\frac 1N \sum_i (x_i-y_i)^2$$ and $$ NMSE(x,y)=MSE(x,y)/MSE(x,0) = \frac{\| x-y\|_2^2}{\| ...
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1answer
523 views

Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
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2answers
229 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
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2answers
720 views

Scale Space - Scales and Octaves

So I'm desperately trying to understand scale space for signals, specifically for 2D images... I'm having trouble with algorithms that discuss creating a pyramid. Specifically, I don't understand how ...
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1answer
20 views

find period of discrete cosine

let us consider following we should find period of this discrete signal,for periodicity we should have $x[n+kN]=x[n]$ or $10\cos(0.088\pi(n+kN) +\phi)=10\cos(0.088\pi n+\phi)$ or $0.088\pi ...
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0answers
9 views

Is there a standard way for modeling a Kalman filter where the measurements are obtained from differences?

Consider for simplicity a Kalman filter applied to the one-dimensional state space model $x_{n}=f_{n}x_{n-1}+q_{n}$ $y_{n}=h_{n}x_{n}+r_{n}$ with white noise errors. Assume that $r_n=e_n-e_{n-1}$ ...
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2answers
1k views

Adjustable Sigmoid Curve (S-Curve) from (0,0) to (1,1)

I feel like this is such a simple question but I am at such a loss. I currently have a set of values that I would like to weigh by an S Curve. My data ranges from $0$ to $1$ and never leaves those ...
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0answers
19 views

Total change of a signal overtime

I have some signals whose analytic type I do not know. I can only sample them every 0.1 secs. I want to pick that signal that changes as little as possible. For example, between sin2t and sint I ...
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0answers
27 views

Do 2 timeseries represent the input better than one?

I only have a very basic familiarity with signal processing and information theory so I'm sorry if this is a very straight forward question. I have a very brief input signal and two timeseries as ...
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1answer
28 views

Discrete Time Fourier Transform of a real signal

I want to prove that if we have a real signal x[n] then for the DTFT it is applied that we have an even symmetry: | X(Ω+1/10) | = | X(-(Ω+1/10)) | (I mean the ...
2
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1answer
45 views

Trigonometric regression

What methods are performed for regression with trigonometric functions? E.g. : Sequence: $$-1, 0, 1, -1, 0, 1, \text{.....}$$ Regression: ...
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1answer
297 views

Calculate phase and amplitude of a sampled sine wave

I have an electronics project where I sample two sine waves. I would like to know what the amplitude (peak) and difference in phase is. Actually I just need to know the average product of the two ...
3
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1answer
38 views

Image Reconstruction:Phase vs. Magnitude

Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. $$ ...
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0answers
30 views

Expectation and convolution question.

I am learning in an image processing course, and the professor did the following: As part of a derivation, has this: What I do not understand, is how he was able to remove $r(i,j)$ to the ...
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2answers
57 views

Fourier Transform: why do all segments generate the same magnitude response?!

I'm working on a DTMF program, and what I've done is to break the one long input signal I initially receive into a bunch of smaller components. I perform an FFT on each of the small components and ...
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1answer
29 views

A relationship among multiple periodic arrays

There are N periodic arrays ai[n] with period Ti, respectively, where i=1, 2, … , N. Each array has a property that a[n]=1 when n=k*T where k is integer, otherwise a[n]=0. Then a new array is created ...
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1answer
30 views

Blind deconvolution of a function convolved with itself

I have a function/vector $f$ that I know is the result of an unknown function $g$ convolved with itself: $f = g \ast g$ Is there any way to do a blind deconvolution on $f$ with this constraint?
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1answer
984 views

How to determine the step response using convolution of the signal's impulse response?

The step response can be determined by recalling that the response of an LTI to any input signal is found by computing the convolution of that signal with the impulse response of the system. ...
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1answer
40 views

Vctor of sine signal [closed]

How to create a vector of sine signal (I am looking for an example such a function which can create such vector) thanks
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1answer
114 views

Approximate Periodic Function by shifting Basis Functions

Given a periodic "Target Function" $F(t)$ a set of $N$ periodic "Basis Functions" $B_i(t)$ of arbitrary shape All functions are defined on the same interval $T$. I am allowed to shift ...
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0answers
28 views

On the truncation of spherical harmonics

Suppose there is a function $f(\theta,\phi)$ defined on the surface of a sphere, and $\theta$ and $\phi$ are the polar and azimuthal angles respectively. Similar with the fact that a function defined ...
0
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1answer
33 views

Signal processing and properties question

We have the relationship between input and output: $Y(k)=|x(k+1)| + x(k)+ kx(k-5)$. Find the output of the system when $x(k)=d(k)$. What does this output represent? Show if the system is linear, ...
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0answers
23 views

Solution to iterative equation with floor operation

This question is motivated by the following signal processing problem. Suppose there is a source, which produces vectors of data of length $N_s$, and a filter (or other subsystem) that accepts ...
2
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0answers
104 views

Deriving Isosensitivity Functions in ROC space from elementary signal detection parameters

In signal detection, an observer is assigned the task of discerning the presence (or absence) of some signal with accompanying noise. There are four possible outcomes: a hit ($H$), a miss, a false ...
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1answer
33 views

How can I plot this signal

What will be the value of this signal (specified as impulse train) , say for values of t from 0 to 6 $$g(t)=\sum_{k=- \infty }^\infty \delta(t-2k)$$
2
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1answer
24 views

Problem about average of cos square (nt) where n is arbitrary

I often see people just say time average of cos^2(nwt) is 1/2, I want to know in what cases this is not valid? w is just the frequency, can be assumed as a constant. Assuming you are always ...
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1answer
37 views

Query regarding phase of analytic signal.

Using the following matlab commands, phase of analytic signal can be obtained. sig_a = hilbert ( sig ) ; ph = atan(angle(sig_a)) ; As for as my understanding is angle(sig_a) will give phase of ...
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0answers
41 views

Function with bounded derivative as ODE

Given a function $x(t)$, I am looking for a function $y(t)$ which closely follows $x(t)$ except that its derivative must be bounded by a constant $c$, i.e. $\dot{y} \leq c$. Is there a way to describe ...
2
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1answer
60 views

Moving average as ODE

Is it possible to represent or approximate the moving average $m(t) = \frac{1}{w}\int_{t-w}^t x(\tau) d\tau$ of a function $x(t)$ as a set of ordinary differential equations $\dot{y} = \ldots$? I am ...
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1answer
40 views

Fourier and $Z$ transform of a signal?

We have $$X(k)=4[u(k-2)-u(k)* d(k-3)]$$ I need to find the Fourier transform,$Z$ transform,as well as dhe magnitude and phase spectra. First of all I think that I need to convert the $u(k)$ and ...
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0answers
17 views

How to evaluate the difference between two classes of data which are highly overlapped

I’m trying to implement a classifier based on a dataset comprising two classes of high dimensional time-series observations (the values of the two classes of observations are highly similar). I ...
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0answers
33 views

Plotting the frequency spectrum of a signal

I've found this algorithm here on Mathematica.SE to plot the frequencies of a signal using Fourier. It works beautifully, but I'm having some trouble understanding ...
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1answer
37 views

How do we determine the duration of a fundamental frequency using the DFT (or FFT)?

I'm still in the process of learning the details of the DFT (and FFT) and I've just made a test .wav file in Audacity by joining 3 one-second sine waves together. .wav file 1 = 440 Hz, sample rate ...
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1answer
45 views

Essential mathematics for Image Processing

What are the most essential mathematical concepts one has to be familiar with for succeeding in the field of Image/Signal Processing and Machine Learning. I am somewhat familiar with Tensors, ...
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1answer
39 views

Impulse response and z transform question?

We have $g(k)=\{ [(1/5)^k]u(k)\text{ for $1 \le k\le3$ and $0$ for other }k\}$ The input is $x(k)=\delta(k) +3\delta(k-1)+ \delta(k-2) $ Using Z transform we have to find the output $y(k)$ and the ...
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1answer
12 views

Representing a real sampled signal with N samples as a complex sampled signal with N/2 samples

I am studying the discrete Fourier transform, and in its most basic definition it is an invertible linear transformation on the complex numbers. From Wikipedia: The sequence of $N$ complex numbers ...
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1answer
24 views

Differential equations signal theory question?

We have the system in the figure.I have to find the differential equation that describes the system.Now,the equation is x(k-1)-y(k-1)=y(k),but I don't understand why.I mean I have studied systems and ...
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1answer
56 views

If $tf(t)=tg(t)$, where $f(t), g(t)$ are distributions, then $f(t)=g(t)+λδ(t)$.

Using Dirac distribution properties, prove that if $tf(t)=tg(t)$, where $f(t), g(t)$ are distributions, then $f(t)=g(t)+λδ(t)$. If someone knows please help me how to start the proof. Thank you
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0answers
28 views

Expected Value With Signum

So I am trying to show convergence of a filter, and in order for it to converge, I need the following condition to hold: $ E\{ \mathbf{s} x sgn(\mathbf{h}^{T} \mathbf{s} x) \} \; \alpha \; E \{ ...
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1answer
27 views

Discrete Function Approximation Error - Which type? (Applied math, signals)

I have two functions, one derived via software, and we can call it the exact function, $f_{exact}$. The other is a result I got through hardware, and we can call it the approximation, $f_{approx}$. ...
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2answers
37 views

Compressive Sensing matrix

I am working with compressive sensing recovery with image and I test with various sensing matrices: Case 1: Sensing matrix A of size MxN is i.i.d Gaussian matrix. Case 2: Sensing matrix A is size of ...